Optimizing the Mean Swimming Velocity of a Model Two-sphere Swimmer

TL;DR

This paper analytically and numerically investigates how to optimize the mean swimming velocity of a two-sphere swimmer in a viscous fluid, considering inertial and frictional effects, and compares different modeling approaches.

Contribution

It introduces an analytical expression for the mean swimming velocity of a two-sphere swimmer including inertial effects and compares simplified models with more detailed calculations.

Findings

Optimal stroke frequency and radius ratio maximize velocity.

Analytical and numerical results show good agreement.

Model comparisons highlight the importance of inertial effects.

Abstract

The swimming of a two-sphere system oscillating in a viscous fluidis studied on the basis of simplified equations of motion which take account of both friction and inertial effects. In the model the friction follows from an Oseen approximation to the mobility matrix, and the inertial effects follow from a dipole approximation to the added mass matrix. The resulting mean swimming velocity is evaluated analytically in a first harmonics approximation. For specific choices of the parameters this is compared with the exact result following from a numerical calculation including higher harmonics. The Oseen-Dipole model is compared with the simpler Oseen* model, in which the added mass effects are approximated by just the effective mass of the single spheres and dipole interactions are neglected. The expression for the mean swimming velocity can be reduced to a dimensionless scaling form. For given viscosity and mass density of the fluid the frequency of the stroke and the ratio of radii can be chosen such that the swimming velocity is optimized.